Phase2_SlopeStabilityVerification_Part1

Phase2

2D elasto-plastic finite element program

for slope and excavation stability analyses

Slope Stability Verification Manual

Part I

© 1989 - 2011 Rocscience Inc.

TABLE OF CONTENTS

INTRODUCTION 1

1 SIMPLE SLOPE STABILITY ASSESSMENT 2

2 NON-HOMOGENEOUS SLOPE 4

3 NON-HOMOGENEOUS SLOPE WITH SEISMIC LOAD 6

4 DRY SLOPE STABILITY ASSESSMENT OF TALBINGO DAM 8

5 WATER TABLE WITH WEAK SEAM 10

6 SLOPE WITH LOAD AND PORE PRESSURE DEFINED BY WATER TABLE 12

7 SLOPE WITH PORE PRESSURE DEFINED BY DIGITIZED TOTAL HEAD GRID 15

8 SLOPE STABILITY WITH A PORE PRESSURE GRID 17

9 PORE PRESSURE GRID WITH TWO LIMIT SETS 19

10 SIMPLE SLOPE STABILITY ASSESSMENT II 22

11 LAYERED SLOPE STABILITY ASSESSMENT 24

12 SIMPLE SLOPE WITH WATER TABLE 27

13 SIMPLE SLOPE III 30

14 SIMPLE SLOPE WITH PORE PRESSURE DEFINED BY RU VALUE 33

15 LAYERED SLOPE II 35

16 LAYERED SLOPE AND A WATER TABLE WITH WEAK SEAM 37

17 SLOPE WITH THREE DIFFERENT PORE PRESSURE CONDITIONS 39

18 SLOPE WITH 3 DIFFERENT PORE PRESSURE CONDITIONS AND A WEAK SEAM 41

19 UNDRAINED LAYERED SLOPE 44

20 SLOPE WITH VERTICAL LOAD (PRANDTL’S WEDGE) 46

21 SLOPE WITH VERTICAL LOAD (PRANDTL’S WEDGE BEARING CAPACITY) 49

22 LAYERED SLOPE WITH UNDULATING BEDROCK 51

23 UNDERWATER SLOPE WITH LINEARLY VARYING COHESION 54

24 LAYERED SLOPE WITH GEOSYNTHETIC REINFORCEMENT 56

25 SYNCRUDE TAILINGS DYKE WITH MULTIPLE PHREATIC SURFACES 60

26 CLARENCE CANNON DAM 63

27 HOMOGENEOUS SLOPE WITH PORE PRESSURE DEFINED BY RU 66

28 FINITE ELEMENT ANALYSIS WITH GROUNDWATER AND STRESS 69

29 HOMOGENEOUS SLOPE STABILITY WITH POWER CURVE STRENGTH CRITERION 73

30 GEOSYNTHETIC REINFORCED EMBANKMENT ON SOFT SOIL 77

31 HOMOGENEOUS SLOPE ANALYSIS COMPARING MOHR-COULOMB AND POWER CURVE STRENGTH CRITERIA 80

32 HOMOGENEOUS SLOPE WITH TENSION CRACK AND WATER TABLE 83

33 HOMOGENEOUS SLOPE ANALYSIS COMPARING MOHR-COULOMB AND POWER CURVE STRENGTH CRITERIA II 86

34 HOMOGENEOUS SLOPE ANALYSIS COMPARING MOHR-COULOMB AND POWER CURVE STRENGTH CRITERIA III 88

REFERENCES 91

1

Introduction This document contains a series of slope stability verification problems that have been analyzed using the shear strength reduction (SSR) technique in Phase2 version 8.0. Results are compared to both Slide version 5.0 limit-equilibrium results and referee values from published sources. These verification tests come from published examples found in reference material such as journal and conference proceedings. For all examples, a short statement of the problem is given first, followed by a presentation of the analysis results, using the SSR finite element method, and various limit equilibrium analysis methods. Full references cited in the verification tests are found at the end of this document. The Phase2 slope stability verification files can be found in your Phase2 installation folder.

2

1 Simple slope stability assessment Introduction

In 1988 a set of 5 basic slope stability problems, together with 5 variants, was distributed both in the Australian Geomechanics profession and overseas as part of a survey sponsored by ACADS (Giam & Donald, 1989). This is the ACADS 1(a) problem.

Problem Description Verification problem #01 for Slide - This problem as shown in Figure 1 is the simple case of a total stress analysis without considering pore water pressures. It represents a homogenous slope with soil properties given in Table 1. The factor of safety and its corresponding critical circular failure is required.

Geometry and Properties

Table 1: Material Properties

c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) 3.0 19.6 20.0

(50,35) (70,35)

(20,25) (30,25)

(20,20) (70,20)

Figure 1 Results (Slide limit-equilibrium results are for a circular slip surface)

Method Factor of Safety SSR (Phase2) 0.99 Bishop (Slide) 0.987 Spencer (Slide) 0.986

GLE (Slide) 0.986 Janbu Corrected (Slide) 0.990

Note: Referee Factor of Safety = 1.00 [Giam] Mean Bishop FOS (18 samples) = 0.993 Mean FOS (33 samples) = 0.991

3

Figure 2 – Solution Using SSR

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Maximum Total Displacement [m]

Shear Strength ReductionCritical SRF: 0.995 at Displacement: 0.019 m

ConvergedFailed to Converge

Figure 3 – SSR Convergence Graph

4

2 Non-Homogeneous Slope Introduction

In 1988 a set of 5 basic slope stability problems, together with 5 variants, was distributed both in the Australian Geomechanics profession and overseas as part of a survey sponsored by ACADS (Giam & Donald, 1989). This is the ACADS 1(c) problem.

Problem description

Verification problem #03 for Slide - This problem models a non-homogeneous, three layer slope with material properties given in Table 1. The factor of safety and its corresponding critical circular failure surface is required.



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Soil #1 0.0 38.0 19.5 Soil #2 5.3 23.0 19.5 Soil #3 7.2 20.0 19.5

(50,35) (70,35)

(54,31) soil #1 (70,31) (50,29) soil #2 (20,25) (40,27) (30,25) (52,24) (70,24) soil #3

(20,20) (70,20) Figure 1

Results (Slide limit-equilibrium results are for a circular slip surface)



Note : Referee Factor of Safety = 1.39 [Giam] Mean Bishop FOS (16 samples) = 1.406 Mean FOS (31 samples) = 1.381

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3 Non-Homogeneous Slope with Seismic Load Introduction

In 1988 a set of 5 basic slope stability problems, together with 5 variants, was distributed both in the Australian Geomechanics profession and overseas as part of a survey sponsored by ACADS (Giam & Donald, 1989). This is the ACADS 1(d) problem.

Problem description Verification problem #04 for Slide - This problem models a non-homogeneous, three layer slope with material properties given in Table 1 and geometry as shown in Figure 1. A horizontal seismically induced acceleration of 0.15g is included in the analysis. The factor of safety and its corresponding critical circular failure surface is required.



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Soil #1 0.0 38.0 19.5 Soil #2 5.3 23.0 19.5 Soil #3 7.2 20.0 19.5

(50,35) (70,35)

(54,31) soil #1 (70,31) (50,29) soil #2 (20,25) (40,27) (30,25) (52,24) (70,24) soil #3

(20,20) (70,20) Figure 1




Note : Referee Factor of Safety = 1.00 [Giam] Mean FOS (15 samples) = 0.973

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4 Dry slope stability assessment of Talbingo Dam Introduction


Problem description

Verification problem #05 for Slide - Talbingo Dam is shown in Figure 1. The material properties for the end of construction stage are given in Table 1 while the geometrical data are given in Table 2.


Table 1: Material Properties c΄ (kN/m2) φ΄ (deg.) γ (kN/m3)

Rockfill 0 45 20.4 Transitions 0 45 20.4 Filter 0 45 20.4 Core 85 23 18.1

Table 2: Geometry Data

Pt.# Xc (m) Yc (m) Pt.# Xc (m) Yc (m) Pt.# Xc (m) Yc (m) 1 0 0 10 515 65.3 19 307.1 0 2 315.5 162 11 521.1 65.3 20 331.3 130.6 3 319.5 162 12 577.9 31.4 21 328.8 146.1 4 321.6 162 13 585.1 31.4 22 310.7 0 5 327.6 162 14 648 0 23 333.7 130.6 6 386.9 130.6 15 168.1 0 24 331.3 146.1 7 394.1 130.6 16 302.2 130.6 25 372.4 0 8 453.4 97.9 17 200.7 0 26 347 130.6 9 460.6 97.9 18 311.9 130.6 - - -

2 3 4 5 21 24

16 18 20 23 26 7 6 9 8 10 11 1 12 13 15 17 19 22 25 14

Figure 1

Rockfill Transitions

Core Filter (very thin seam)

9


Note : Referee Factor of Safety = 1.95 [Giam] Mean FOS (24 samples) = 2.0

Figure 2 Solution Using SSR

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Figure 3 –SSR Convergence Graph



10

5 Water Table with Weak Seam Introduction


Problem description

Verification problem #07 for Slide - This problem has material properties given in Table 1, and is shown in Figure 1. The water table is assumed to coincide with the base of the weak layer. The effect of negative pore water pressure above the water table is to be ignored. (i.e. u=0 above water table).



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Soil #1 28.5 20.0 18.84 Soil #2 0 10.0 18.84

(67.5,40) (84,40) Soil #2 (seam) Soil #1 (20,27.75) (43,27.75) (84,27) (20,27) (20,26.5) Soil #1 (84,26.5) (20,20) (84,20)

Figure 1 Results

Method Factor of Safety SSR (Phase2) 1.26

Spencer 1.258 GLE 1.246

Janbu Corrected 1.275 Note : Referee Factor of Safety = 1.24 – 1.27 [Giam] Mean Non-circular FOS (19 samples) = 1.293

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6 Slope with Load and Pore Pressure Defined by Water Table Introduction

In 1988 a set of 5 basic slope stability problems, together with 5 variants, was distributed both in the Australian Geomechanics profession and overseas as part of a survey sponsored by ACADS (Giam & Donald, 1989). This is the ACADS 4 problem.

Problem description

Verification problem #09 for Slide - The geometry is shown in Figure 1. The soil parameters, external loadings and piezometric surface are shown in Table 1, Table 2 and Table 3 respectively. The effect of a tension crack is to be ignored.



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Soil #1 28.5 20.0 18.84 Soil #2 0 10.0 18.84

Table 2: External Loadings

Xc (m) Yc (m) Normal Stress (kN/m2) 23.00 27.75 20.00 43.00 27.75 20.00 70.00 40.00 20.00 80.00 40.00 40.00

Table 3: Data for Piezometric surface

Pt.# Xc (m) Yc (m) 1 20.0 27.75 2 43.0 27.75 3 49.0 29.8 4 60.0 34.0 5 66.0 35.8 6 74.0 37.6 7 80.0 38.4 8 84.0 38.4

Pt.# : Refer to Figure 1

13

Figure 1 - Geometry Results – (Side results use Monte-Carlo optimization)

Method Factor of Safety SSR 0.69


Janbu Corrected 0.700 Note: Referee Factor of Safety = 0.78 [Giam] Mean Non-circular FOS (20 samples) = 0.808 Referee GLE Factor of Safety = 0.6878 [Slope 2000]

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7 Slope with Pore Pressure Defined by Digitized Total Head Grid Introduction

In 1988 a set of 5 basic slope stability problems, together with 5 variants, was distributed both in the Australian Geomechanics profession and overseas as part of a survey sponsored by ACADS (Giam & Donald, 1989). This is the ACADS 5 problem.

Problem description

Verification problem #10 for Slide - Geometry is shown in Figure 1. The soil properties are given in Table 1. This slope has been excavated at a slope of 1:2 (β=26.56˚) below an initially horizontal ground surface. The position of the critical slip surface and the corresponding factor of safety are required for the long term condition, i.e. after the ground water conditions have stabilized. Pore water pressures may be derived from the given boundary conditions or from the approximate flow net provided in Figure 2.



11.0 28.0 20.00

Excavation (15,35) Initial Ground Level (50,35) (95,35)

(15,33) Initial W.T. Level Final Ground Profile (15,26) (32,26) (15,25) (30,25) Final External Water level (15,20) (95,20)

Figure 1

Figure 2

16

Results Note: Referee Factor of Safety = 1.53 [Giam] Mean FOS (23 samples) = 1.464


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Bishop 1.498 Spencer 1.501

GLE 1.500 Janbu Corrected 1.457

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8 Slope Stability with a Pore Pressure Grid Introduction

This problem is an analysis of the Saint-Alban embankment (in Quebec) which was built and induced to failure for testing and research purposes in 1972 (Pilot et. al, 1982).

Problem description

Verification problem #11 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1. The position of the critical slip surface and the corresponding factor of safety are required. Pore water pressures were derived from the given equal pore pressure lines on Figure 1. using the Thin-Plate Spline interpolation method.



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Embankment 0 44.0 18.8

Clay Foundation 2 28.0 16.68 (0,12) (8,12)

Embankment

(0,8) (14,8) (22,8) u=0 kPa (0,7.5) (9,6.75) (22,7.5) (0,6.5) u=30 kPa (4,6.5) (15.25,6) (18,5.75) (0,5.5) u=60 kPa (4,5.5) (9,6) (22,5.5) (9,5) (0,4.25) u=90 kPa (4,4.25) (14.75,4)

(18,3.25) (14.5,2) (22,3) Clay Foundation (18,0.75) (22,0.5) (22,0)

Figure 1

Material Barrier (0,8), (14,8)

18

Results Note: Referee Factor of Safety = 1.04 [Pilot]


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9 Pore Pressure Grid with Two Limit Sets Introduction

This problem is an analysis of the Cubzac-les-Ponts embankment (in France) which was built and induced to failure for testing and research purposes in 1974 (Pilot et.al, 1982).

Problem description

Verification problem #13 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1. Pore water pressure was derived from the data in Table 2 using the Thin Plate Spline interpolation method. Verification is for a deep failure so support of the face is required since the factor of safety against embankment face failure is 1.11. This is accomplished by using a thin layer of elastic (infinite strength) material on the face of the embankment.



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Embankment 0 35 21.2 Upper Clay 10 24 15.5 Lower Clay 10 28.4 15.5

Table 2: Water Pressure Points

Pt.# Xc (m) Yc (m) u (kPa) Pt.# Xc (m) Yc (m) u (kPa) Pt.# Xc (m) Yc (m) u (kPa) 1 11.5 4.5 125 16 16 7.2 25 31 24.5 7.2 25 2 11.5 5.3 100 17 18 2.3 125 32 27 3.1 100 3 11.5 6.8 50 18 18 5.3 100 33 27 6.1 50 4 11.5 7.2 25 19 18 6.8 50 34 27 7.2 25 5 12.75 3.35 125 20 18 7.2 25 35 29.75 1.55 100 6 12.75 5.2 100 21 20 1.15 125 36 29.75 5.55 50 7 12.75 6.8 50 22 20 4.85 100 37 29.75 7.2 25 8 12.75 7.2 25 23 20 6.8 50 38 32.5 0 100 9 14 2.3 125 24 20 7.2 25 39 32.5 5 50 10 14 5.1 100 25 22 0 125 40 32.5 7.2 25 11 14 6.8 50 26 22 4.4 100 41 37.25 4.7 50 12 14 7.2 25 27 22 6.8 50 42 37.25 6.85 25 13 16 2.3 125 28 22 7.2 25 43 42 4.4 50 14 16 5.2 100 29 24.5 3.75 100 44 42 6.5 25 15 16 6.8 50 30 24.5 6.45 50 45 - - -

20

(0,13.5) (20,13.5) Embankment (0,9) (26.5,9) (44,9) (0,8) 4 8 12 16 20 24 28 31 (44,8) (0,6) Upper Clay 3 7 11 15 19 23 27 34 37 40 42 44 2 6 10 14 18 30 33 36 (44,6)

1 22 26 39 41 43 Lower Clay 5 29 32 9 13 17

21 25 35 38 Results




Note: Author’s Factor of Safety (by Bishop method) = 1.24 [Pilot]

Figure 1

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10 Simple Slope Stability Assessment II Introduction

This model is taken from Arai and Tagyo (1985) example#1 and consists of a simple slope of homogeneous soil with zero pore pressure.

Problem description

Verification problem #14 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1. There are no pore pressures in this problem.



soil 41.65 15 18.82

Figure 1 - Geometry Results

Method Factor of Safety (circular surface)

Factor of Safety (non-circular surface)

SSR 1.40 Bishop 1.409 --

Janbu Simplified 1.319 1.253 Janbu Corrected 1.414 1.346

Spencer 1.406 1.388 Arai and Tagyo (1985) Bishops Simplified Factor of Safety = 1.451 Arai and Tagyo (1985) Janbu Simplified Factor of Safety = 1.265 Arai and Tagyo (1985) Janbu Corrected Factor of Safety = 1.357

user

Sticky Note

pokusati u PAK-u sta daje, pa uporediti.

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11 Layered Slope Stability Assessment

Introduction This model is taken from Arai and Tagyo (1985) example#2 and consists of a layered slope where a layer of low resistance is interposed between two layers of higher strength. A number of other authors have also analyzed this problem, notably Kim et al. (2002), Malkawi et al. (2001), and Greco (1996).

Problem description

Verification problem #15 for Slide - Problem geometry is shown in Figure 1. The material properties are given in Table 1. The factor of safety calculated using SSR and compared to limit equilibrium results of both circular and noncircular slip surfaces. There are no pore pressures in this problem.



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Upper Layer 29.4 12 18.82 Middle Layer 9.8 5 18.82 Lower Layer 294 40 18.82

Figure 1 – Geometry

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Results



SSR 0.39 Bishop 0.421 --


Spencer 0.424 0.412 Arai and Tagyo (1985) Bishops Simplified Factor of Safety = 0.417 Kim et al. (2002) Bishops Simplified Factor of Safety = 0.43 Greco (1996) Spencers method using monte carlo searching = 0.39 Kim et al. (2002) Spencers method using random search = 0.44 Kim et al. (2002) Spencers method using pattern search = 0.39 Arai and Tagyo (1985) Janbu Simplified Factor of Safety = 0.405 Arai and Tagyo (1985) Janbu Corrected Factor of Safety = 0.430


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12 Simple Slope with Water Table Introduction

This model is taken from Arai and Tagyo (1985) example#3 and consists of a simple slope of homogeneous soil with pore pressure.

Problem description

Verification problem #16 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1. The location for the water table is shown in Figure 1. The factor of safety calculated using SSR and compared to limit equilibrium results of both circular and noncircular slip surfaces. Pore pressures are calculated assuming hydrostatic conditions. The pore pressure at any point below the water table is calculated by measuring the vertical distance to the water table and multiplying by the unit weight of water. There is zero pore pressure above the water table.



soil 41.65 15 18.82

Figure 1 - Geometry

28

Results



SSR 1.09 Bishop 1.117 --


Spencer 1.118 1.094 Arai and Tagyo (1985) Bishops Simplified Factor of Safety = 1.138 Arai and Tagyo (1985) Janbu Simplified Factor of Safety = 0.995 Arai and Tagyo (1985) Janbu Corrected Factor of Safety = 1.071


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13 Simple Slope III Introduction

This model is taken from Yamagami and Ueta (1988) and consists of a simple slope of homogeneous soil with zero pore pressure. Greco (1996) has also analyzed this slope.

Problem description

Verification problem #17 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1. The factor of safety calculated using SSR and compared to limit equilibrium results of both circular and noncircular slip surfaces. There are no pore pressures in this problem.



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) soil 9.8 10 17.64

Figure 1 - Geometry

31

Results



SSR 1.33 Bishop 1.344 --

Ordinary 1.278 -- Janbu Simplified -- 1.178

Spencer -- 1.324 Yamagami and Ueta (1988) Bishops Simplified Factor of Safety = 1.348 Yamagami and Ueta (1988) Fellenius/Ordinary Factor of Safety = 1.282 Yamagami and Ueta (1988) Janbu Simplified Factor of Safety = 1.185 Yamagami and Ueta (1988) Spencer Factor of Safety = 1.339 Greco (1996) Spencer Factor of Safety = 1.33


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14 Simple Slope with Pore Pressure Defined by Ru Value Introduction

This model is taken from Baker (1980) and was originally published by Spencer (1969). It consists of a simple slope of homogeneous soil with pore pressure.

Problem description

Verification problem #18 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1. The position of the critical slip surface and the corresponding factor of safety are calculated for a noncircular slip surface. The pore pressure within the slope is modeled using an Ru value of 0.5.


Table 1: Material Properties c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Ru

soil 10.8 40 18 0.5

Figure 1 - Geometry

34

Results – Slide result using Random search with Monte-Carlo optimization

Baker (1980) Spencer Factor of Safety = 1.02 Spencer (1969) Spencer Factor of Safety = 1.08


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Spencer (Slide) 1.01

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15 Layered Slope II Introduction

This model is taken from Greco (1996) example #4 and was originally published by Yamagami and Ueta (1988). It consists of a layered slope without pore pressure.

Problem description

Verification problem #19 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1.



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Upper Layer 49 29 20.38

Layer 2 0 30 17.64 Layer 3 7.84 20 20.38

Bottom Layer 0 30 17.64

Figure 1 - Geometry

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Results

Greco (1996) Spencer Factor of Safety = 1.40 - 1.42 Spencer (1969) Spencer Factor of Safety = 1.40 - 1.42

Figure 2 - Solution Using SSR

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Figure 3 - SSR Convergence Graph


Spencer (Slide) 1. 398

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16 Layered Slope and a Water Table with Weak Seam Introduction

This model is taken from Greco (1996) example #5 and was originally published by Chen and Shao (1988). It consists of a layered slope with pore pressure and a weak seam.

Problem description

Verification problem #20 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1. The factor of safety calculated using SSR and compared to limit equilibrium results of both circular and noncircular slip surfaces. The weak seam is modeled as a 0.5m thick material layer at the base of the model.



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Layer 1 9.8 35 20 Layer 2 58.8 25 19 Layer 3 19.8 30 21.5 Layer 4 9.8 16 21.5

Figure 1 - Geometry

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Results Method Factor of Safety

(circular surface) Factor of Safety

(non-circular surface) SSR (Phase2) 1.02 Bishop (Slide) 1.087 -- Spencer (Slide) 1.093 1.007

Greco (1996) Spencer factor of safety for nearly circular local critical surface = 1.08 Chen and Shao (1988) Spencer Factor of Safety = 1.01 - 1.03 Greco (1996) Spencer Factor of Safety = 0.973 - 1.1


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17 Slope with Three Different Pore Pressure Conditions

Introduction This model is taken from Fredlund and Krahn (1977). It consists of a homogeneous slope with three separate water conditions, 1) dry, 2) Ru defined pore pressure, 3) pore pressures defined using a water table. The model is done in imperial units to be consistent with the original paper. Quite a few other authors, such as Baker (1980), Greco (1996), and Malkawi (2001) have also analyzed this slope.

Problem description

Verification problem #21 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1. The position of the circular slip surface is given in Fredlund and Krahn as being xc=120,yc=90,radius=80. The GLE/Discrete Morgenstern and Price method was run with the half sine interslice force function.

Table 15.1: Material Properties

c΄ (psf) φ΄ (deg.) γ (pcf) Ru (case2) soil 600 20 120 0.25

Figure 1 - Geometry

Results

Case Ordinary (F&K)

Ordinary (Slide)

Bishop (F&K)

Bishop (Slide)

Spencer (F&K)

Spencer (Slide)

M-P (F&K)

M-P (Slide)

SSR (Phase2)

1-Dry 1.928 1.931 2.080 2.079 2.073 2.075 2.076 2.075 2.0 2-Ru 1.607 1.609 1.766 1.763 1.761 1.760 1.764 1.760 1.68 3-WT 1.693 1.697 1.834 1.833 1.830 1.831 1.832 1.831 1.78

40

Figure 2 Solution Using SSR – Case 3 with water table

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Maximum Total Displacement [ft]

Shear Strength ReductionCritical SRF: 1.78 at Displacement: 0.101 ft


Figure 3 –SSR Convergence Graph – Case 3 with water table

41

18 Slope with 3 Different Pore Pressure Conditions and a Weak Seam

Introduction This model is taken from Fredlund and Krahn (1977). It consists of a slope with a weak layer and three separate water conditions, 1) dry, 2) Ru defined pore pressure, 3) pore pressures defined using a water table. The model is done in imperial units to be consistent with the original paper. Quite a few other authors, such as Kim and Salgado (2002), Baker (1980), and Zhu, Lee, and Jiang (2003) have also analyzed this slope. Unfortunately, the location of the weak layer is slightly different in all the above references. Since the results are quite sensitive to this location, results routinely vary in the second decimal place.

Problem description

Verification problem #22 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1. The position of the composite circular slip surface is given in Fredlund and Krahn as being xc=120,yc=90,radius=80. The GLE/Discrete Morgenstern and Price method was run with the half sine interslice force function.

Table 16.1: Material Properties

c΄ (psf) φ΄ (deg.) γ (pcf) Ru (case2) Upper soil 600 20 120 0.25 Weak layer 0 10 120 0.25


42

Results (Slide limit-equilibrium results are for a Composite Circular) Case 1: Dry Slope

Method Slide Fredlund & Krahn

Zhu, Lee, and Jiang

SSR

Ordinary 1.300 1.288 1.300

1.34 Bishop Simplified 1.382 1.377 1.380

Spencer 1.382 1.373 1.381 GLE/Morgenstern-Price 1.372 1.370 1.371 Case 2: Ru


Zhu, Lee, and Jiang

SSR

Ordinary 1.039 1.029 1.038


Spencer 1.124 1.118 1.119 GLE/Morgenstern-Price 1.114 1.118 1.109 Case 3: Water Table


Zhu, Lee, and Jiang

SSR

Ordinary 1.174 1.171 1.192


Spencer 1.244 1.245 1.261 GLE/Morgenstern-Price 1.237 1.245 1.254

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Figure 2 Solution Using SSR – Case 3 with water table (contour range: 0 – 0.02)

Figure 3 –SSR Convergence Graph – Case 3 with water table

44

19 Undrained Layered Slope Introduction

This model is taken from Low (1989). It consists of a slope with three layers with different undrained shear strengths.

Problem description

Verification Problem #24 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1.


Cu (KN/m2) γ (KN/m3) Upper Layer 30 18 Middle Layer 20 18 Bottom Layer 150 18

Figure 1 – Geometry Results – (Slide limit-equilibrium results are for circular auto refine search)

Low (1989) Ordinary Factor of Safety=1.44 Low (1989) Bishop Factor of Safety=1.44


Ordinary (Slide) 1.439 Bishop (Slide) 1.439

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20 Slope with Vertical Load (Prandtl’s Wedge) Introduction

This model is taken from Chen and Shao (1988). It analyses the classical problem in the theory of plasticity of a weightless, frictionless slope subjected to a vertical load. This problem was first solved by Prandtl (1921)

Problem description

Verification Problem #25 for Slide - Geometry is shown in Figure 1. The slope geometry, equation for the critical load, and position of the critical slip surface is defined by Prandtl and shown in Figure 1. The critical failure surface has a theoretical factor of safety of 1.0. The analysis uses the input data of Chen and Shao and is shown in Table 1. The geometry, shown in Figure 2, is generated assuming a 10m high slope with a slope angle of 60 degrees. The critical uniformly distributed load for failure is calculated to be 149.31 kN/m, with a length equal to the slope height, 10m.



c (kN/m2) φ (deg.) γ (kN/m3) soil 49 0 1e-6

Figure 1 – Closed-form solution (Chen and Shao, 1988)

47

Figure 2 Geometry Results


Spencer (Slide) 1. 051 GLE/M-P (Slide) 1. 009 Chen and Shao (1988) Spencer Factor of Safety = 1.05

48


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Shear Strength ReductionCritical SRF: 1 at Displacement: 0.026 m



49

21 Slope with Vertical Load (Prandtl’s Wedge Bearing Capacity) Introduction

This verification test models the well-known Prandtl solution of bearing capacity:

qc=2C(1+π/2)

Problem description Verification problem #26 for Slide - Geometry is shown in Figure 1. The material properties are given in Table 1. With cohesion of 20kN/m2, qc is calculated to be 102.83 kN/m. A uniformly distributed load of 102.83kN/m was applied over a width of 10m as shown in the below figure. The theoretical noncircular critical failure surface was used.



c (kN/m2) φ (deg.) γ (kN/m3) soil 20 0 1e-6

Figure 1 Geometry

Results


Spencer (Slide) 0.941 Theoretical factor of safety=1.0

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22 Layered Slope with Undulating Bedrock Introduction

This model was taken from Malkawi, Hassan and Sarma (2001) who took it from the XSTABL version 5 reference manual (Sharma 1996). It consists of a 2 material slope overlaying undulating bedrock. There is a water table and moist and saturated unit weights for one of the materials. The other material has zero strength. The model is done with imperial units (feet,psf,pcf) to be consistent with the original XSTABL analysis.

Problem description Verification problem #27 for Slide is shown in Figure 1. The material properties are given in Table 1. One of the interesting features of this model is the different unit weights of soil 1 below and above the water table. Another factor is the method of pore-pressure calculation. The pore pressures are calculated using a correction for the inclination of the phreatic surface and steady state seepage. Phase2, Slide and XSTABL allow you to apply this correction. The pore pressures tend to be smaller than if a static head of water is assumed (measured straight up to the phreatic surface from the center of the base of a slice). Since Phase2 does not allow for a saturated and moist unit weight, the more conservative saturated unit weight is used. Phase2 does not allow for zero strength materials, this plays havoc with the plasticity calculations in a finite-element analysis. To solve this problem, a distributed load is used to replace the influence of soil 2 as shown in Figure 2.


Table 1: Material Properties c (psf) φ (deg.) γ moist (pcf) γ saturated (pcf)

Soil 1 500 14 116.4 124.2 Soil 2 0 0 116.4 116.4


52

Figure 2 – Phase2 Model Results (Circular analysis in Slide)



GLE/M-P (half-sine) 1.51

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Figure 3 – Phase2 SSR Maximum Shear Strain Plot

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23 Underwater Slope with Linearly Varying Cohesion Introduction

This model is taken from Duncan (2000). It looks at the failure of the 100 ft high underwater slope at the Lighter Aboard Ship (LASH) terminal at the Port of San Francisco.

Problem description

Verification #29 for Slide - Geometry is shown in Figure 1. All geoemetry and property values are determined using the figures and published data in Duncan (2000). The cohesion is taken to be 100 psf at an elevation of -20 ft and increase linearly with depth at a rate of 9.8 psf/ft. The stability of the bench is of interest, thus the material above elevation -20 and to the right of the bench (x>350) is given elastic properties (can’t fail).


Table 1: Material Properties cohesion

(datum) (psf)

Datum (ft)

Rate of change (psf/ft)

Unit Weight

(pcf) San Francisco Bay Mud 100 -20 9.8 100

Figure 1 - Geometry

55

Results

Duncan (2000) quotes a factor of safety of 1.17.

Figure 2 – Phase2 SSR Maximum Shear Strain Plot

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Method Deterministic Factor of Safety

SSR (Phase2) 1.12 Janbu Simplified 1.13 Janbu Corrected 1.17


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24 Layered Slope with Geosynthetic Reinforcement Introduction

This model is taken from Borges and Cardoso (2002), their case 3 example. It looks at the stability of a geosynthetic-reinforced embankment on soft soil.

Problem description

Verification problem #32 for Slide - Geometry is shown in Figures 1 and 2. The sand embankment is modeled as a Mohr-Coulomb material while the foundation material is a soft clay with varying undrained shear strength. The geosynthetic has a tensile strength of 200 KN/m, and frictional resistance against slip of 30.96 degrees. The reinforcement force is assumed to be parallel with the reinforcement. There are two embankment materials, the lower embankment material is from elevation 0 to 1 while the upper embankment material is from elevation 1 to either 7 (Case 1) or 8.75m (Case 2). The geosynthetic is at elevation 0.9, just inside the lower embankment material.



c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Upper Embankment 0 35 21.9 Lower Embankment 0 33 17.2

Cu (kN/m2) γ

(kN/m3) Clay1 43 18 Clay2 31 16.6 Clay3 30 13.5 Clay4 32 17 Clay5 32 17.5

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Figure 1 – Case 1 – Embankment height = 7m

Figure 2 – Case 2 – Embankment height = 8.75m

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Results – Case 1 – Embankment height = 7m

Factor of Safety

SSR 1.15 Circle A (Slide) 1.23

Circle A (Borges) 1.25 Circle B (Slide) 1.22

Circle B (Borges) 1.19

Figure 3 – Case 1 – Shear Strain plot, failed geotextile shown in red

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Figure 4 – Case 1 – SSR Convergence Graph

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Results – Case 2 – Embankment height = 8.75m Factor of

Safety SSR 0.95

Circle C (Slide) 0.98 Circle C (Borges) 0.99

Figure 5 – Case 2 – Shear Strain plot, failed geotextile shown in red

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Figure 6 – Case 2 – SSR Convergence Graph

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25 Syncrude Tailings Dyke with Multiple Phreatic Surfaces Introduction

Verification #25 comes from El-Ramly et al (2003). It looks at the assessment of the factor of safety of a Syncrude tailings dyke in Canada.

Problem description

Verification problem #33 for Slide - The original model from the El-Ramly et al paper is shown in Figure 1. The input parameters for the Phase2 model are provided in Table 1. The Phase2 model is shown on Figure 2. As in the El-Ramly et al paper, the Bishop simplified analysis method is used for the Slide analysis.

Figure 1


Material c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Tailing sand (TS) 0 34 20 Glacio-fluvial sand (Pf4) 0 34 17 Sandy till (Pgs) 0 34 17 Disturbed clay-shale (Kca) 0 7.5 17

61


Figure 2a

Figure 2b

Tailing sand (TS) Glacio-fluvial sand (Pf4)

Sandy till (Pgs)

Disturbed clay-shale (Kca)

Phreatic surface in TS

Phreatic surface in Pf4

Critical surfaces analyzed

Note: Phreatic Surfaces do not intersect at toe

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Results

Factor of Safety

SSR 1.29 Slide (Bishop) 1.305 El-Ramly et al 1.31

Figure 3 – Shear Strain plot

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26 Clarence Cannon Dam Introduction

This model is taken from Wolff and Harr (1987). It is a model of the Clarence Cannon Dam in north eastern Missouri, USA. This verification compares factor of safety results from Phase2, Slide and those determined by Wolff and Harr for a non-circular critical surface.

Problem description

Verification problem #34 for Slide - Wolff and Harr evaluate the factor of safety against failure of the Cannon Dam along the specified non-circular critical surface shown on Figure 1 (taken from their paper). Properties are given in Table 1. The Phase2 model is shown on Figure 2.

Figure 1

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Figure 2

Table 1: Material Properties*

Material c΄ (lb/ft2) φ΄ (deg.) γ (lb/ft3) Phase I fill 2,230 6.34 150 Phase II fill 2,901.6 14.8 150 Sand drain 0 30 120

*Information on the non-labeled soil layers in the model shown on Figure 2 is omitted because it has no influence on the factor of safety of the given critical surface.

Phase II fill

Sand drain

Phase I fill

Critical failure surface

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Results

Deterministic Factor of Safety

SSR 2.29 Slide (GLE method) 2.333

Slide (Spencer method) 2.383 Wolff and Harr 2.36


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27 Homogeneous Slope with Pore Pressure Defined by Ru Introduction

This model is taken from Li and Lumb (1987) and Hassan and Wolff (1999). It analyzes a simple homogeneous slope with pore pressure defined using Ru.

Problem description

Verification problem # 36 for Slide - The geometry of the homogeneous slope is shown in Figure 1 and material parameters are provided in Table 1.


Figure 1


Property Mean value c΄ (kN/m2) 18 φ΄ (deg.) 30 γ (kN/m3) 18

ru 0.2

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Results Deterministic

Factor of Safety SSR 1.31

Slide (Bishop method) 1.339 Hasssan and Wolf 1.334


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28 Finite Element Analysis with Groundwater and Stress Introduction

Verification #28 models a typical steep cut slope in Hong Kong. The example is taken from Ng and Shi (1998). It illustrates the use of finite element groundwater and stress analysis in the assessment of the stability of the cut.

Problem description

Verification problem #38 for Slide - The cut has a slope face angle of 28o and consists of a

24m thick soil layer, underlain by a 6m thick bedrock layer. Figure 1 describes the slope model.

Figure 1 Model geometry Steady-state groundwater analysis is conducted using the finite element module in Phase2. Initial conditions of constant total head are applied to both sides of the slope. Three different initial hydraulic boundary conditions (H=61m, H=62m, H=63m) for the right side of the slope are considered for the analyses in this section, Figure 1. Constant hydraulic boundary head of 6m is applied on the left side of the slope. Figure 2 shows the soil permeability function used to model the hydraulic conductivity of the soil, Ng (1998).

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Figure 2 – Hydraulic conductivity function*

The negative pore water pressure, which is commonly refereed to as the matrix suction of soil, above the water table influences the soil shear strength and hence the factor of safety. Ng and Shi used the modified Mohr-Coulomb failure criterion for the unsaturated soils, which can be written as:

bwaan uuuc ϕϕστ tan)(tan)( '' −+−+= where nσ is the normal stress, bϕ is an angle defining the increase in shear strength for an increase in matrix suction of the soil. Table 1 shows the material properties for the soil. * The raw data for Figure 2 can be found in the verification data file.

Table 1 Material properties

'c (kPa) 'ϕ (deg.) bϕ (deg.) γ (kN/m3) 10 38 15 16

Both positive and negative pore water pressures predicted from groundwater analysis engine were used in the stability analysis. To match the results, the extent of the failure is limited to a region close to the cut. The region is limited by using an elastic (infinite strength) material outside this region.

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Results

H

(total head at right side of slope)

Phase2(SSR) Slide Ng. & Shi (1998)

61m 1.64 1.616 1.636

62m 1.55 1.535 1.527

63m 1.41 1.399 1.436

Figure 3 –Shear Strain plot (H=61m)

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Figure 4 – SSR Convergence Graph (H=61m)

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29 Homogeneous Slope Stability with Power Curve Strength Criterion Introduction

This model is taken from Tandjiria (2002), their problem 1 example. It looks at the stability of a geosynthetic-reinforced embankment on soft soil. The problem looks at the stability of the embankment if it consists of either a sand fill or an undrained clayey fill. Both are analyzed.

Problem description

Verification problem #29 is shown in Figures 1 and 2. The purpose of this example is to compute the required reinforcement force to yield a factor of safety of 1.35. Both circular and non-circular surfaces are looked at. In each case, the embankment is modeled without the reinforcement; the critical slip surface is located, and then used in the reinforced model to determine the reinforcement force to achieve a factor of safety of 1.35. This is done for a sand or clay embankment, circular and non-circular critical slip surfaces. Both cases incorporate a tension crack in the embankment. In the case of the clay embankment, a water-filled tension crack is incorporated into the analysis. The reinforcement is located at the base of the embankment. The model was analyzed with both Spencer and GLE (half-sine interslice function) but Spencer was used for the force computation. The reinforcement is modeled as an active force since this is how Tandjiria et.al. modelled the force.



Cu/c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Clay Fill Embankment 20 0 19.4 Sand Fill Embankment 0 37 17 Soft Clay Foundation 20 0 19.4

Figure 1 - Sand Fill Embankment

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Figure 2 - Clay Fill Embankment

Results – Sand embankment with no reinforcement

Method Factor of Safety SRF 1.25

Circular Limit-Equilibrium Spencer 1.209

GLE/M-P 1.218 Tandjiria (2002) Spencer 1.219

Non-circular Limit-Equilibrium Spencer 1.189

GLE/M-P 1.196 Tandjiria (2002) Spencer 1.192

Figure 3 – Shear Strain Plot for Sand Fill Embankment

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Figure 4 – SSR Convergence Graph for Sand Fill Embankment

Results – Clay embankment with no reinforcement

Method Factor of Safety SRF 0.99 Circular Limit-Equilibrium

Spencer 0.975 GLE/M-P 0.975

Tandjiria (2002) Spencer 0.981 Non-circular Limit-Equilibrium

Spencer 0.932 GLE/M-P 0.941

Tandjiria (2002) Spencer 0.941

Figure 5 – Shear Strain Plot for Clay Fill Embankment

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Figure 6 – SSR Convergence Graph for Clay Fill Embankment

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30 Geosynthetic Reinforced Embankment on Soft Soil Introduction

This problem was taken from J. Perry (1993), Fig. 10. It involves material for which the relationship between effective normal stress and shear stress is described by the non-linear power curve.

Problem Description This problem analyzes a simple homogeneous slope (Fig. 1). The dry soil is assumed to have non-linear power curve strength parameters. The computed factor of safety and failure surface obtained from the SRF method are compared to those given by Janbu limit-equilibrium analysis of the non-linear surface shown in Fig. 2.



Parameter Value A 2 b 0.7

γ (kN/m3) 20.0

Figure 1

78

Figure 2

Results

Method Factor of Safety SRF 0.91

SLIDE Janbu Simplified 0.944 Note: Referee Factor of Safety = 0.98 [Perry]

Figure 3 – Shear Strain Plot

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31 Homogeneous Slope Analysis Comparing Mohr-Coulomb and Power Curve Strength Criteria Introduction

This problem was taken from Baker (2003). It is his first example problem comparing linear and non-linear Mohr envelopes.

Problem Description Verification problem #31 compares two homogeneous slopes of congruent geometry (Figure 1) under different strength functions (Table 1). The factor of safety is determined for the Mohr-Coulomb and Power Curve strength criteria. The power curve criterion used by Baker has the non-linear form:

n

aa T

PAP

+=

στ … Pa = 101.325 kPa

The factor of safety was determined using the material properties that Baker derives from his iterative process; these values should be compared to the accepted values.


Table 1: Material Properties Material c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) A n T

Clay 11.64 24.7 18 0.58 0.86 0 Clay, iterative results 0.39 38.6 18 -- -- --

Figure 1 - Geometry

Results Strength Type Method Factor of Safety Power Curve SRF (Generalized Hoek-Brown) 1.11

Janbu Simplified 0.92 Spencer 0.96

Mohr-Coulomb SRF 1.53 Janbu Simplified 1.47

Spencer 1.54 Mohr-Coulomb with iteration results

(c΄ = 0.39 kPa, φ΄ = 38.6 °) SRF 0.98

Janbu simplified 0.96 Spencer 0.98

Baker (2003) non-linear results: FS = 0.97 Baker (2003) M-C results: FS = 1.50

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Figure 2 – Shear Strain Plot for Mohr-Coulomb criterion

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Figure 3 – SSR Convergence Graph for Mohr-Coulomb Criterion

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Figure 4 – Shear Strain Plot for Power Curve Criterion

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Figure 5 – SSR Convergence Graph for Power Curve Criterion

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32 Homogeneous Slope with Tension Crack and Water Table Introduction

This problem was taken from Baker (2003). It is his second example problem comparing linear and non-linear Mohr envelopes.

Problem Description Verification problem #45, (#56 for Slide) compares two homogeneous slopes of congruent geometry (Figure 1) under different strength functions (Table 1). The critical circular surface factor of safety and maximum effective normal stress must be determined for both Mohr-Coulomb strength criterion and Power Curve criterion. The power curve criterion was derived from Baker’s own non-linear function:

n

aa T

PAP

+=

στ … Pa = 101.325 kPa

The power curve variables are in the form: ( ) cda b

n ++= στ Finally, the critical circular surface factor of safety and maximum effective normal stress must be determined using the material properties that Baker derives from his iterative process; these values should be compared to the accepted values.


Table 1: Material Properties Material c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) A n T

Clay 11.64 24.7 18 0.58 0.86 0 Clay, iterative results 0.39 38.6 18 -- -- --

Figure 1 - Geometry

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Results Strength Type Method Factor of Safety Power Curve SRF 2.74

Janbu Simplified (Circular) 2.56 Spencer (Circular) 2.66

Mohr-Coulomb SRF 2.83 Janbu Simplified (Circular) 2.66

Spencer (Circular) 2.76 Baker (2003) non-linear results: FS = 2.64

Baker (2003) M-C results: FS = 2.66

Figure 2 – Shear Strain Plot for Power Curve Criterion.

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Figure 4 – Shear Strain Plot for Mohr-Coulomb Criterion.

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33 Homogeneous Slope Analysis Comparing Mohr-Coulomb and Power Curve Strength Criteria II Introduction

In December 2000, Pockoski and Duncan released a paper comparing eight different computer programs for analysis of reinforced slopes. This is their second test slope.

Description Verification Problem #33 analyses an unreinforced homogeneous slope. A water table is present, as is a dry tension crack (Figure 1). The circular critical failure surface and factor of safety for this slope are required (40x40 grid).


Table 1: Material Properties Material c΄ (psf) φ΄ (deg.) γ (pcf)

Sandy clay 300 30 120

Figure 1 - Geometry

Figure 2 - Geometry

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Results

Method SRF SLIDE UTEXAS4 SLOPE/W WINSTABL XSTABL RSS SRF 1.28 -- -- -- -- -- --

Spencer -- 1.30 1.29 1.29 1.32 -- -- Bishop simplified -- 1.29 1.28 1.28 1.31 1.28 1.28 Janbu simplified -- 1.14 1.14 1.14 1.18 1.23 1.13 Lowe-Karafiath -- 1.31 1.31 -- -- -- --

Ordinary -- 1.03 -- 1.02 -- -- -- SNAIL FS = 1.18 (Wedge method) GOLD-NAIL FS = 1.30 (Circular method)

Figure 3 – Shear Strain Plot

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

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34 Homogeneous Slope Analysis Comparing Mohr-Coulomb and Power Curve Strength Criteria III Introduction

This problem was taken from Baker (2003). It is his third example problem comparing linear and non-linear Mohr envelopes.

Description Verification problem #34 compares two homogeneous slopes of congruent geometry (Figure 1) under different strength functions (Table 1 and 2). The critical circular surface factor of safety and maximum effective normal stress must be determined for both Mohr-Coulomb strength criterion and Power Curve criterion. The power curve criterion was derived from Baker’s own non-linear function:

n

aa T

PAP

+=

στ … Pa = 101.325 kPa

The power curve variables are in the form: ( ) cda b

n ++= στ Finally, the critical circular surface factor of safety and maximum effective normal stress must be determined using the material properties that Baker derives from his iterative process; these values should be compared to the accepted values.


Table 1: Material Properties – Power Curve criterion Baker’s Parameters SLIDE Parameters

Material A n T a b c d Clay 0.535 0.6 0.0015 3.39344 0.6 0 0.1520

Table 2: Material Properties – Mohr-Coulomb criterion

Material c΄ (kN/m2) φ΄ (deg.) γ (kN/m3) Clay 6.0 32 18

Figure 1 - Geometry

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Results Strength Type Method Factor of Safety Power Curve SRF 1.47

Janbu Simplified 1.35 Spencer 1.47

Mohr-Coulomb SRF 1.38 Janbu Simplifed 1.29 Spencer 1.37

Baker (2003) non-linear results: FS = 1.48 Baker (2003) M-C results: FS = 1.35

Figure 2 – Shear Strain Plot for Mohr-Coulomb Criterion

1.0

1.1

1.2

1.3

1.4

1.5

1.6

-0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15

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Figure 4 – Shear Strain Plot for Power Curve Criterion

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

-0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17

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